Optimal Lipschitz estimates for the ¯ equation on a class of convex domains

Viêt Anh Nguyên; El Hassan Youssfi

Annales de la Faculté des sciences de Toulouse : Mathématiques (2003)

  • Volume: 12, Issue: 2, page 179-243
  • ISSN: 0240-2963

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Nguyên, Viêt Anh, and Youssfi, El Hassan. "Optimal Lipschitz estimates for the $\overline{\partial }$ equation on a class of convex domains." Annales de la Faculté des sciences de Toulouse : Mathématiques 12.2 (2003): 179-243. <http://eudml.org/doc/73602>.

@article{Nguyên2003,
author = {Nguyên, Viêt Anh, Youssfi, El Hassan},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {-equation; Lipschitz estimates},
language = {eng},
number = {2},
pages = {179-243},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Optimal Lipschitz estimates for the $\overline\{\partial \}$ equation on a class of convex domains},
url = {http://eudml.org/doc/73602},
volume = {12},
year = {2003},
}

TY - JOUR
AU - Nguyên, Viêt Anh
AU - Youssfi, El Hassan
TI - Optimal Lipschitz estimates for the $\overline{\partial }$ equation on a class of convex domains
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2003
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 12
IS - 2
SP - 179
EP - 243
LA - eng
KW - -equation; Lipschitz estimates
UR - http://eudml.org/doc/73602
ER -

References

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  1. [1] Berndtsson ( B. ). — A formula for interpolation and division in Cn, Math. Ann.263, p. 399-418 (1983). Zbl0499.32013MR707239
  2. [2] Bonami ( A. ) and Charpentier ( P.). - Solutions de l'équation ∂ et zéros de la classe de Nevanlinna dans certains domaines faiblement pseudo-convexes , Ann. Inst. Fourier.32(4), p. 53-89 (1982). Zbl0493.32005MR694128
  3. [3] Charpentier ( P.). - Formules explicites pour les solutions minimales de l'équation ∂u = f dans la boule et dans le polydisque de Cn, Ann. Inst. Fourier.30(4), p. 121-154 (1980). Zbl0425.32009MR599627
  4. [4] Chen ( Z.) , Krantz ( S.G.) and Ma ( D.). — Optimal Lp estimates for the ∂ equation on complex ellipsoids in Cn, Manuscripta math.80, p. 131-149 (1993). Zbl0789.32011MR1233477
  5. [5] Cumenge ( A. ). — Estimées Lipschitz optimales dans les convexes de type fini, C. R. Acad. Sci. Paris325, p. 1077-1080 (1997). Zbl0904.32013MR1614008
  6. [6] Cumenge ( A. ).— Sharp estimates for ∂ on convex domains of finite type, Ark. Mat.39, p. 1-25 (2001). Zbl1028.35115MR1807801
  7. [7] Diederich ( K.), Fischer ( B.) and Fornæss ( J.E.). - Hõlder estimates on convex domains of finite type, Math. Z.232, p. 43-61 (1999). Zbl0932.32008
  8. [8] Fischer ( B. ) . - Lp estimates on convex domains of finite type, Math. Z.236, p. 401-418 (2001). Zbl0984.32022MR1815835
  9. [9] Greiner ( P. ) and Stein ( E.). - "Estimates for the ∂-Neumann problem", Mathematical Notes19, Princeton University Press, (1977 ). Zbl0354.35002MR499319
  10. [10] Hefer ( T. ).— Hõlder and LP estimates for ∂ on convex domains of finite type depending on Catlin's multitype, Math. Z.242, p. 367-398 (2002). Zbl1048.32024
  11. [11] Krantz ( S.G. ). — Optimal Lipschitz and LP regularity for the equation ∂u = f on strongly pseudo-convex domains, Math. Annalen.219, p. 233-260 (1976). Zbl0303.35059MR397020
  12. [12] Krantz ( S.G. ). — Estimates for integral kernels of mixed type, fractional integration operators, and optimal estimates for the ∂ operator, Manuscripta math. 30, p. 21-52 (1979). Zbl0417.35057MR552362
  13. [13] Krantz ( S.G. ). — Characterizations of various domains of holomorphy via ∂ estimates and applications to a problem of Kohn, Illinois. Journal Math.23(2), p. 267-285 (1979). Zbl0394.32009MR528563
  14. [14] Lelong ( P. ) and Gruman ( L.). - "Entire functions of several complex variables", Grundlehren der Mathematischen Wissenschaften282, Springer-Verlag, (1986). Zbl0583.32001MR837659
  15. [15] Mengotti ( G.) and Youssfi ( E.H.). - The weighted Bergman projection and related theory on the minimal ball, Bull. Sci. math.123, p. 501-525 (1999). Zbl0956.32006MR1713302
  16. [16] Rudin ( W. ). - "Function theory in the unit ball of Cn ", Grundlehren der Mathematischen Wissenschaften241, Springer-Verlag, New York-Berlin, 1980. Zbl0495.32001MR601594
  17. [17] Viêt Anh ( N.).— Fatou and Korányi-Vági type theorems on the minimal balls, Publ. Mat.46, 49-75 (2002). Zbl1013.32006MR1904856
  18. [18] Viêt Anh ( N.) and Youssfi ( E.H.). - Lipschitz estimates for the ∂-equation on the minimal ball, Michigan Math. J.49, p. 299-323 (2001). Zbl1011.32026MR1852305
  19. [19] Viêt Anh ( N.) and Youssfi ( E.H.). - Estimations Lipschitziennes optimales pour l'équation ∂ dans une classe de domaines convexes, C. R. Acad. Sci. Paris t. 332, Série I, p. 1065-1070 (2001). Zbl0997.32037MR1847481
  20. [20] Youssfi ( E.H.). — Proper holomorphic liftings and new formulas for the Bergman and Szegõ kernels, Stud. Math.152, 161-186 (2002). Zbl1013.32003

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